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Annales scientifiques de l'ENS - Parutions - série 4, 50 (2017)

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ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 50, fascicule 2 (2017)

Olivier Taïbi
Dimensions of spaces of level one automorphic forms for split classical groups using the trace formula
Annales scientifiques de l'ENS 50, fascicule 2 (2017), 269-344

Télécharger cet article : Fichier PDF

Résumé :
Dimensions des espaces de formes automorphes en niveau un pour les groupes classiques déployés à l'aide de la formule des traces
Nous démontrons des formules explicites pour le nombre de représentations automorphes cuspidales algébriques régulières et essentiellement auto-duales pour les groupes linéaires sur Q, comme fonction des poids de Hodge. Nous en déduisons des formules explicites pour les dimensions des espaces de formes modulaires de Siegel cuspidales à valeurs vectorielles.

Mots-clefs : Formule des traces d'Arthur-Selberg, intégrales orbitales, algorithme, endoscopie, paquets d'Adams-Johnson, formes modulaires de Siegel.

Abstract:
We derive explicit formulae for the number of level one, regular algebraic and essentially self-dual automorphic cuspidal representations of general linear groups over Q, as a function of the Hodge weights. As a consequence, we obtain formulae for dimensions of spaces of vector-valued Siegel modular cusp forms.

Keywords: Arthur-Selberg trace formula, orbital integrals, algorithm, endoscopy, Adams-Johnson packets, Siegel modular forms.

Class. math. : 11F72, 11Y40, 11R39, 11F46, 22E47, 11-04.


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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